{
  "id": "2310.11474",
  "version": "v1",
  "published": "2023-10-17T02:55:32.000Z",
  "updated": "2023-10-17T02:55:32.000Z",
  "title": "Viscosity solutions to HJB equations associated with optimal control problem for McKean-Vlasov SDEs",
  "authors": [
    "Jinghai Shao"
  ],
  "comment": "28 pages. arXiv admin note: text overlap with arXiv:2310.10950",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "This work concerns the optimal control problem for McKean-Vlasov SDEs. In order to characterize the value function, we develop the viscosity solution theory for Hamilton-Jacobi-Bellman (HJB) equations on the Wasserstein space using Mortensen's derivative. In particular, a comparison principle for viscosity solution is established. Our approach is based on Borwein-Preiss variational principle to overcome the loss of compactness for bounded sets in the Wasserstein space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-17T02:55:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "35Q93",
      "49L25"
    ],
    "keywords": [
      "optimal control problem",
      "mckean-vlasov sdes",
      "hjb equations",
      "wasserstein space",
      "borwein-preiss variational principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}